Herd immunity and epidemic size in networks with vaccination homophily.

We study how the herd immunity threshold and the expected epidemic size depend on homophily with respect to vaccine adoption. We find that the presence of homophily considerably increases the critical vaccine coverage needed for herd immunity and that strong homophily can push the threshold entirely out of reach. The epidemic size monotonically increases as a function of homophily strength for a perfect vaccine, while it is maximized at a nontrivial level of homophily when the vaccine efficacy is limited. Our results highlight the importance of vaccination homophily in epidemic modeling.

Adaptive and optimized COVID-19 vaccination strategies across geographical regions and age groups.

We evaluate the efficiency of various heuristic strategies for allocating vaccines against COVID-19 and compare them to strategies found using optimal control theory. Our approach is based on a mathematical model which tracks the spread of disease among different age groups and across different geographical regions, and we introduce a method to combine age-specific contact data to geographical movement data. As a case study, we model the epidemic in the population of mainland Finland utilizing mobility data from a major telecom operator. Our approach allows to determine which geographical regions and age groups should be targeted first in order to minimize the number of deaths. In the scenarios that we test, we find that distributing vaccines demographically and in an age-descending order is not optimal for minimizing deaths and the burden of disease. Instead, more lives could be saved by using strategies which emphasize high-incidence regions and distribute vaccines in parallel to multiple age groups. The level of emphasis that high-incidence regions should be given depends on the overall transmission rate in the population. This observation highlights the importance of updating the vaccination strategy when the effective reproduction number changes due to the general contact patterns changing and new virus variants entering.

Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history.

The origin of non-Poissonian or bursty temporal patterns observed in various data sets for human social dynamics has been extensively studied, yet its understanding still remains incomplete. Considering the fact that humans are social beings, a fundamental question arises: Is the bursty human dynamics dominated by individual characteristics or by interaction between individuals? In this paper we address this question by analyzing the Wikipedia edit history to see how spontaneous individual editors are in initiating bursty periods of editing, i.e., individual-driven burstiness, and to what extent such editors' behaviors are driven by interaction with other editors in those periods, i.e., interaction-driven burstiness. We quantify the degree of initiative (DoI) of an editor of interest in each Wikipedia article by using the statistics of bursty periods containing the editor's edits. The integrated value of the DoI over all relevant timescales reveals which is dominant between individual-driven and interaction-driven burstiness. We empirically find that this value tends to be larger for weaker temporal correlations in the editor's editing behavior and/or stronger editorial correlations. These empirical findings are successfully confirmed by deriving an analytic form of the DoI from a model capturing the essential features of the edit sequence. Thus our approach provides a deeper insight into the origin and underlying mechanisms of bursts in human social dynamics.

Interactions of water confined in a metal-organic framework as studied by a combined approach of Raman, FTIR, and IR electroabsorption spectroscopies and multivariate curve resolution analysis.

Water in nanoconfinement shows distinct properties that are markedly different from those of bulk water. These unique properties stem not only from the water-water interaction but also from the interactions between water and the surrounding confining environment. Here we used a combined approach of vibrational spectroscopies (Raman, FTIR, and IR electroabsorption) and a multivariate curve resolution technique to study the interactions of water in a heterogeneous confining environment within a prototype of pillared layer-type metal-organic frameworks (MOFs), CPL-1 ([Cu2(pzdc)2(pyz)]n, where pzdc = 2,3-pyrazinedicarboxylate, pyz = pyrazine). The OH stretching Raman spectrum of hydrated CPL-1 microcrystals revealed that the adsorbed water molecules resemble the subpopulation of bulk water whose hydrogen bond is weak. Multivariate curve resolution analysis of FTIR spectra monitoring water desorption from CPL-1 allowed for accurate assignments of the framework's carboxylate vibrational modes associated with water-filled and empty nanopores of the MOF, and for quantitative determination of the number fraction of these pores. Furthermore, building on the assignments so made, IR electroabsorption measurements showed that the hydrogen-bonding interaction with water adsorbed in CPL-1 has little impact on the response to electric fields of the framework vibrational modes. The present findings altogether provide a solid basis of elucidating water confined in CPL-1 and demonstrate the potential of the combined vibrational spectroscopic method for interrogating the interactions within MOFs.

Burst-tree decomposition of time series reveals the structure of temporal correlations.

Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial for understanding the underlying mechanisms behind such temporal patterns. Among them bursty event sequences have been studied mostly in terms of interevent times (IETs), while the higher-order correlation structure between IETs has gained very little attention due to the lack of a proper characterization method. In this paper we propose a method of representing an event sequence by a burst tree, which is then decomposed into a set of IETs and an ordinal burst tree. The ordinal burst tree exactly captures the structure of temporal correlations that is entirely missing in the analysis of IET distributions. We apply this burst-tree decomposition method to various datasets and analyze the structure of the revealed burst trees. In particular, we observe that event sequences show similar burst-tree structure, such as heavy-tailed burst-size distributions, despite of very different IET distributions. This clearly shows that the IET distributions and the burst-tree structures can be separable. The burst trees allow us to directly characterize the preferential and assortative mixing structure of bursts responsible for the higher-order temporal correlations. We also show how to use the decomposition method for the systematic investigation of such correlations captured by the burst trees in the framework of randomized reference models. Finally, we devise a simple kernel-based model for generating event sequences showing appropriate higher-order temporal correlations. Our method is a tool to make the otherwise overwhelming analysis of higher-order correlations in bursty time series tractable by turning it into the analysis of a tree structure.

Copula-based algorithm for generating bursty time series.

Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. Modeling and simulating various dynamical processes requires us to generate event sequences with a heavy-tailed IET distribution and memory effects between IETs. For this, we propose a Farlie-Gumbel-Morgenstern copula-based algorithm for generating event sequences with correlated IETs when the IET distribution and the memory coefficient between two consecutive IETs are given. We successfully apply our algorithm to the cases with heavy-tailed IET distributions. We also compare our algorithm to the existing shuffling method to find that our algorithm outperforms the shuffling method for some cases. Our copula-based algorithm is expected to be used for more realistic modeling of various dynamical processes.

Correlated bursts in temporal networks slow down spreading.

Spreading dynamics has been considered to take place in temporal networks, where temporal interaction patterns between nodes show non-Poissonian bursty nature. The effects of inhomogeneous interevent times (IETs) on the spreading have been extensively studied in recent years, yet little is known about the effects of correlations between IETs on the spreading. In order to investigate those effects, we study two-step deterministic susceptible-infected (SI) and probabilistic SI dynamics when the interaction patterns are modeled by inhomogeneous and correlated IETs, i.e., correlated bursts. By analyzing the transmission time statistics in a single-link setup and by simulating the spreading in Bethe lattices and random graphs, we conclude that the positive correlation between IETs slows down the spreading. We also argue that the shortest transmission time from one infected node to its susceptible neighbors can successfully explain our numerical results.

Limits of the memory coefficient in measuring correlated bursts.

Temporal inhomogeneities in event sequences of natural and social phenomena have been characterized in terms of interevent times and correlations between interevent times. The inhomogeneities of interevent times have been extensively studied, while the correlations between interevent times, often called correlated bursts, are far from being fully understood. For measuring the correlated bursts, two relevant approaches were suggested, i.e., memory coefficient and burst size distribution. Here a burst size denotes the number of events in a bursty train detected for a given time window. Empirical analyses have revealed that the larger memory coefficient tends to be associated with the heavier tail of the burst size distribution. In particular, empirical findings in human activities appear inconsistent, such that the memory coefficient is close to 0, while burst size distributions follow a power law. In order to comprehend these observations, by assuming the conditional independence between consecutive interevent times, we derive the analytical form of the memory coefficient as a function of parameters describing interevent time and burst size distributions. Our analytical result can explain the general tendency of the larger memory coefficient being associated with the heavier tail of burst size distribution. We also find that the apparently inconsistent observations in human activities are compatible with each other, indicating that the memory coefficient has limits to measure the correlated bursts.

Order-disorder transition in repulsive self-propelled particle systems.

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the system undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze the binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at a dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.